Degrees of Freedom of Connected Compasses

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Discussion Overview

The discussion revolves around determining the degrees of freedom of a connected pair of compasses, exploring both theoretical and conceptual aspects of the problem. Participants examine the implications of rigid connection, needle orientation, and forces acting on the compasses.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant suggests that if the compasses are rigidly connected, there are three degrees of translation, three degrees of rotation, and two compass needle positions.
  • Another participant argues that the needles will always be parallel due to their configuration, while a different reply counters that equilibrium does not guarantee constant parallelism.
  • Some participants mention the effects of N-N repulsion and N-S attraction, but express differing views on their relevance to the degrees of freedom.
  • A participant points out the ambiguity in the term "pair of compasses," indicating that the vagueness complicates the discussion.
  • Another participant notes that they are receiving inconsistent results when attempting to analyze the problem.

Areas of Agreement / Disagreement

Participants express disagreement regarding the parallelism of the compass needles and the relevance of magnetic forces to the degrees of freedom. The discussion remains unresolved with multiple competing views present.

Contextual Notes

The discussion highlights limitations due to vague terminology and assumptions about the configuration and behavior of the compasses, which may affect the analysis of degrees of freedom.

AbhiFromXtraZ
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What will be the degrees of freedom of a ''Connected pair of compasses''?
 
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Assuming they are rigidly connected then three degrees of translation, three degrees of rotation, and two compass needle positions.
 
Have you thought about this?
The needles will always be parallel.
This is not a simple concept. There will be N-N repulsion and N-S attraction.
 
AbhiFromXtraZ said:
Have you thought about this?

Don't be rude.

AbhiFromXtraZ said:
The needles will always be parallel.

Just because their equilibrium positions are parallel does not mean they will always be parallel.
 
AbhiFromXtraZ said:
The needles will always be parallel.
The needles will not always be parallel. I can easily think of scenarios where they are not parallel.

AbhiFromXtraZ said:
There will be N-N repulsion and N-S attraction.
Yes, but that is irrelevant to the question of the number of degrees of freedom.
 
I found that a "pair of compasses" refers to the tool for drawing arcs/circles. This question is so vague it's hard to begin to answer it in a coherent manner.
 
Really the question is so vague...I'm getting different results every time...
 

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